Microscopic Space-Time of Extended Hadrons : Quantum Generalization and Field Equations

摘要

The microlocal space-time of extended hadrons, considered to be anisotropicis specified here as a special Finsler space. For this space the classicalfield equation is obtained from a property of the field on the neighbouringpoints of the autoparallel curve. The quantum field equation has also beenderived for the bispinor field of a free lepton in this Finslerian microspacethrough its quantum generalization below a fundamental length-scale. Thebispinor can be decomposed as a direct product of two spinsors, one dependingon the position coordinates and the other on the directional arguments of theFinsler space. The former one represents the spinor of the macrospace, anassociated Riemannian space-time of the Finsler space, and satisfies the Diracequation. The directional variable-dependent spinor satisfies a differentequation which is solved here. This spinor-part of the bispinor field for aconstituent of the hadron can give rise to an additional quantum number forgenerating the internal symmetry of hadrons. Also, it is seen that in theprocess of separating the bispinor field and its equation an epoch-dependentmass term arises. Although, this part of the particle-mass has no appreciablecontribution in the present era it was very significant for the very earlyperiod of the universe after its creation. Finally, the field equations for aparticle in an external electromagnetic field for this Finslerian microlocalspace-time and its associated Riemannian macrospaces have been found.